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Resonant-superlinear elliptic problems at high-order eigenvalues. (English) Zbl 1466.35217

Summary: This work establishes existence of solution for resonant-superlinear elliptic problems using an appropriate Linking Theorem. The nonlinearity behaves as an asymptotic linear function at \(-\infty\) (resonant or not) and has a superlinear growth at \(+\infty\), with the eventual resonance phenomena occurring in a high order eigenvalue for the associated linear problem. Our main theorems are stated without the well-known Ambrosetti-Rabinowitz condition.

MSC:

35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35J25 Boundary value problems for second-order elliptic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35J20 Variational methods for second-order elliptic equations
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